Transition State Search: P-RFO / Sella

P-RFO maximises the energy along the lowest Hessian eigenvector (the TS mode) and simultaneously minimises along all remaining modes. Activate it with TransitionState true or by including TS on the task: line.

Basic TS Search (P-RFO)

task: TS RHF STO-3G

GEOMETRY
  O   0.000000   0.000000   0.000000
  H   1.100000   0.000000   0.500000
  H  -1.100000   0.000000   0.500000
END

OPT
  Coord     dlc
  MaxCycle  100
END

Sella TS Optimizer

Sella is a saddle-point-aware IC optimizer with TS-BFGS Hessian update and P-RFO step. Combined with TS it targets a first-order saddle point.

Property	`TransitionState true`	`Algorithm sella` + `TransitionState true`
Hessian update	MSP	TS-BFGS
Trust-radius schedule	ρ-based (shrink/grow)	σ-based (multiplicative)
Initial TS Hessian	Lindh (all positive)	Davidson-refined when available
Adaptive eigenvalue check	No	Every 3 steps

Sella Minimum Optimisation

task: SELLA RHF STO-3G

GEOMETRY
  O   0.000000   0.000000   0.100000
  H   0.750000   0.000000  -0.450000
  H  -0.750000   0.000000  -0.450000
END

Sella TS Search with MMF Step (More Robust on Flat Surfaces)

task: TS SELLA RHF STO-3G

GEOMETRY
  O   0.000000   0.000000   0.000000
  H   1.100000   0.000000   0.500000
  H  -1.100000   0.000000   0.500000
END

OPT
  Step     mmf
  Coord    dlc
  SellaOrder 2
  MaxCycle 100
END

Rust Berny TS Optimizer

The Rust Berny optimizer carries its own self-contained transition-state search: partitioned RFO with eigenvector following, flowchart SR1/BFGS/PSB Hessian updates, periodic single-negative-eigenvalue restoration, and conservative saddle-point trust-radius defaults (0.05 Bohr initial, 0.15 Bohr maximum). It works in Cartesian, primitive, delocalized/HDLC, and TRIC coordinate models.

Activate it with Algorithm rberny together with TS, or with the rts shortcut token:

task: TS RHF STO-3G

OPT
  Algorithm rberny
  Coord     dlc
  MaxCycle  100
END

GEOMETRY
  C   -0.621400   -0.081500    0.000000
  N    0.572600   -0.081500    0.000000
  H   -0.201200    1.031500    0.000000
END

Set Step mmf to use the minimum-mode-following saddle-point step (a |H| denominator), which is more robust on flat surfaces and often converges in fewer cycles; the default is partitioned RFO.

Eigenvector following tracks the reaction-coordinate eigenvector across cycles by maximum overlap, so the search keeps climbing the same mode instead of whichever mode is momentarily lowest. The transition-state workflow seeds the optimizer with an exact (or finite-difference) Cartesian Hessian at the starting geometry, so the correct reaction coordinate is identified from the first step; this applies to both Optimize and OptFreq TS jobs.

Verify the Result

A genuine TS shows exactly one imaginary frequency, printed as a negative value:

 Frequencies (cm⁻¹):  -1247.3   1652.1   3825.4

Verify with a FREQ job on the converged TS geometry.

Notes

Starting geometry must be near the transition state
Initial Hessian must have at least one negative eigenvalue for P-RFO
The TS task token implies OPT with TransitionState true
Sella with Step mmf is more robust on flat surfaces (uses |λ| denominator)
Sella TS in DLC space recommended for medium/large molecules

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